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FNCE 3010 (Durham). Fall 2008. Exam 3. Form A.
Multiple choice (3 pts each)
- The positively sloped linear function which illustrates the relationship between an asset’s expected return and its beta coefficient is the:
(a) reward-to-risk ratio. (b) portfolio weight. (c) portfolio risk. (d) Solution: security market line. (e) market risk premium.
- A stock’s risk premium is equal to it’s expected return minus the:
(a) expected market rate of return. (b) Solution: risk-free rate. (c) inflation rate. (d) standard deviation. (e) variance.
- The standard deviation of an asset’s returns is a measure of the asset’s _______ risk.
(a) Solution: total (b) nondiversifiable (c) unsystematic (d) systematic (e) economic
- When a manager estimates the cost of capital for a specific project based on the cost of capital for another firm which specializes in a line of business that is similar to the project, the manager is utilizing the _______ approach.
(a) subjective risk (b) Solution: pure play (c) divisional cost of capital (d) capital adjustment (e) security market line
- The unlevered cost of capital is:
(a) the cost of capital for a firm with no equity in its capital structure. (b) Solution: the cost of capital for a firm that has no debt obligations. (c) equal to the interest tax shield multiplied by the pretax net income. (d) equal to the cost of preferred stock for a firm with no debt. (e) equal to the profit margin for a firm with some debt in its capital structure.
- The value of a firm is maximized when the:
(a) cost of equity is maximized. (b) tax rate is zero. (c) levered cost of capital is maximized. (d) Solution: weighted average cost of capital is minimized. (e) debt-equity ratio is minimized.
- Which form of financing do firms prefer to use first according to the pecking-order theory?
(a) regular debt (b) convertible debt (c) common stock (d) preferred stock (e) Solution: internal funds
Short answer
- (6 points) In this course, we discussed three ways to estimate a firm’s cost of equity. What are they?
Solution: Historical returns, CAPM, DGM.
- (3 points) Given two portfolios with the same expected return, how should an investor decide which is prefer- able?
Solution: The one with the least risk (lowest standard deviation).
- (3 points) Describe the free cash flow hypothesis.
Solution: Firms with large free cash flows are more likely to experience wasteful behavior than firms with low cash flows.
- (6 points) Depending on how risky it is, the appropriate cost of capital for a particular project may differ from that of the firm as a whole. What are the three ways to estimate the appropriate project cost of capital that we discussed in this course?
Solution: Accounting beta approach, pure-play approach, subjective approach.
- (3 points) If you can borrow all of the money you need for a project at 6 percent, does it follow that 6 percent is the project’s cost of capital (Why or why not)?
Solution:
Problems
- (12 points) XYZ Corp. is all equity financed and expects to earn after-tax cash flows of $250 annually forever. The risk profile of these cash flows suggests that they should be discounted at 15%. Now, suppose that XYZ were to issue $400 worth of debt at an interest rate of 5% and use the proceeds to repurchase shares. The tax rate is 35%. Ignore default risk. The risk-free rate is 5% and the market risk premium is 8%.
Based on the levered capital structure:
(a) What is the value of XYZ’s assets?
Solution: 250
- 15 +^
400 · 0. 05 · 0. 35
- 05 = 1667 + 140 = 1807
(b) What is the value of XYZ’s equity?
Solution: 1807 − 400 = 1407
(c) What is XYZ’s expected return on assets?
Solution: 250+400· 0. 05 · 0. 35 1807 =^
257 1807 = 0.^142
(d) What is XYZ’s expected return on equity?
Solution: 257 − 20 1407 =^
237 1407 =^.^168
(e) What does the CAPM imply about XYZ’s equity beta?
Solution: beta = 0.^1680 .− 080.^05 = 1. 475
(f) What is XYZ’s WACC?
Solution: 1407 1807 ·^0 .168 +^
400 1807 ·^0.^05 ·^0 .65 = 0.131 + 0.007 = 0.^138
- (8 points) PQR Corp. is considering a project with an initial cost of $500. The project is expected to generate cash flows of $60 per year forever. The project cash flows are estimated to have a beta of 1.2. The risk-free rate is 4% and the market risk premium is 8%. PQR has a debt-equity ratio of 2, and an equity beta of 1.75. PQR intends to finance the project by issuing new debt. Ignore taxes and default risk. What is the appropriate discount rate to use when evaluating this project?
Solution: 4 + 1. 2 × 8 = 13.6%
What is the NPV of this project?
Solution: −500 + 60/.136 = −$58. 82
Should PQR take on this project?
Solution: No (negative NPV).
- (10 points) XYZ Corp., is all equity financed. Its WACC is 11%. Suppose that it wants to issue some debt in order to expand its operations. It estimates that investors will require a 6% yield in order to hold this debt. After issuing the debt, its debt-equity ratio will be 0.5. The unlevered firm has a beta of 1.2. The tax rate is 34%. Ignore default risk.
(a) What will the cost of equity be for the levered firm?
Solution: RL = RD + (RU − RD ) ×
1 + DE · (1 − T )
(b) What will the levered firm’s WACC be?
Solution: E A ·^ RL^ +^
D A ·^ RD^ ·^ (1^ −^ T^ ) = 0.^667 ·^12 .65 + 0.^333 ·^6 ·^0 .66 = 9.^767
(c) What will the levered firm’s beta be?
Solution: βL = βU ×
1 + DE · (1 − T )
- (8 points) Microsoft Corp. (a computer software company) has decided to branch out from the software business and is considering a project to produce a new line of bicycles. Trek (a bicycle manufacturer) is considering a similar project. In each case, the project involves an initial cost of $1 million and is expected to generate after-tax cash flows of $160,000 per year for 10 years. At the end of that time, the project is ended. There is no salvage value. Suppose that Trek has a debt-equity ratio of 0.5, that its stock has a beta of 1.2, and that its cost of debt is 4%. Also, suppose that Microsoft is all equity financed and has a beta of 0.9. The expected market return is 11% and the risk-free rate is 4%. Ignore taxes and default risk.
Should Trek undertake this project? How about Microsoft? Explain.
Solution: TREK:
R(D) = 4% R(E) = 4 + 1.2 x 7 = 12.4% D/E = 0. WACC = .667 * 12.4 + .333 * 4 = 9.6%
CF(0) = -1M CF(1-10) = 160K NPV(R=9.6%) = 254
Microsoft should also use Trek’s cost of capital (pure play approach). Both companies should accept the project.
- The value of a firm is maximized when the:
(a) cost of equity is maximized. (b) tax rate is zero. (c) levered cost of capital is maximized. (d) Solution: weighted average cost of capital is minimized. (e) debt-equity ratio is minimized.
- Which form of financing do firms prefer to use first according to the pecking-order theory?
(a) regular debt (b) convertible debt (c) common stock (d) preferred stock (e) Solution: internal funds
Short answer
- (6 points) In this course, we discussed three ways to estimate a firm’s cost of equity. What are they?
Solution: Historical returns, CAPM, DGM.
- (3 points) Given two portfolios with the same expected return, how should an investor decide which is prefer- able?
Solution: The one with the least risk (lowest standard deviation).
- (3 points) Describe the free cash flow hypothesis.
Solution: Firms with large free cash flows are more likely to experience wasteful behavior than firms with low cash flows.
- (6 points) Depending on how risky it is, the appropriate cost of capital for a particular project may differ from that of the firm as a whole. What are the three ways to estimate the appropriate project cost of capital that we discussed in this course?
Solution: Accounting beta approach, pure-play approach, subjective approach.
- (3 points) If you can borrow all of the money you need for a project at 6 percent, does it follow that 6 percent is the project’s cost of capital (Why or why not)?
Solution:
No. The cost of capital depends on the risk of the project, not the source of the financing.
- (3 points) According to the pecking order theory, under what conditions should a firm issue new equity?
Solution: Only as a last resort, after exhausting internally generated earnings and debt capacity.
- (5 points) According to a popular legend, what famous inhabitant of the North Pole is responsible for delivering presents to good children on December 25?
- (8 points) PQR Corp. is considering a project with an initial cost of $500. The project is expected to generate cash flows of $60 per year forever. The project cash flows are estimated to have a beta of 1.2. The risk-free rate is 4% and the market risk premium is 8%. PQR has a debt-equity ratio of 2, and an equity beta of 1.75. PQR intends to finance the project by issuing new debt. Ignore taxes and default risk. What is the appropriate discount rate to use when evaluating this project?
What is the NPV of this project?
Should PQR take on this project?
- (12 points) Given a series of monthly returns for RFL, Inc. and the S&P 500, suppose that we estimate the CAPM relationship RA − Rf = β(RM − Rf ) + and obtain β = 1.6, and the standard deviation of the residuals is 1.3.
(a) Using a market risk premium of 8% and risk-free rate of 5%, what is RFL’s risk premium? What is RFL’s expected return?
(b) If the market goes up by 1% next month, what is the expected change in RFL’s stock?
(c) If RFL actually goes up by 2%, what is RFL’s idiosyncratic return for that period?
(d) If the standard deviation of the monthly market return is 4%, what are RFL’s systematic risk, idiosyn- cratic risk, and total risk (expressed as monthly standard deviations)?
(e) What range would I expect RFL’s monthly return to fall within 95% of the time?
(f) Given $1000, describe how to construct a portfolio with a beta of 2 comprised of RFL stock and the risk-free asset. What is the expected annual return for this portfolio?
- (8 points) Microsoft Corp. (a computer software company) has decided to branch out from the software business and is considering a project to produce a new line of bicycles. Trek (a bicycle manufacturer) is considering a similar project. In each case, the project involves an initial cost of $1 million and is expected to generate after-tax cash flows of $160,000 per year for 10 years. At the end of that time, the project is ended. There is no salvage value. Suppose that Trek has a debt-equity ratio of 0.5, that its stock has a beta of 1.2, and that its cost of debt is 4%. Also, suppose that Microsoft is all equity financed and has a beta of 0.9. The expected market return is 11% and the risk-free rate is 4%. Ignore taxes and default risk.
Should Trek undertake this project? How about Microsoft? Explain.
